In the exploration of porous subsurface earth formations around boreholes, it is of significant value to be able to obtain information about the granularity property of the subsurface formation. For example, information which may lead to determination of the presence of small grains, grain size distribution, or grain orientations or changes of these formation parameters from one zone to another can be quite useful in evaluating an earth formation for its ability to yield hydrocarbons.
Proposals have been made to measure mean grain sizes in usually finely grained materials utilizing ultrasonic techniques at scatter frequencies. For example, in articles entitled "Revised Grain-Scattering Formulas and Tables" and "Ultrasonic Attenuation Caused by Scattering in Polycrystalline Metals" by E. P. Papadakis and published in The Journal of the Acoustical Society of America, Volume 37, Number 4, pages 703-717 during April 1965, the frequency and grain size dependence of ultrasonic attenuation are described for a variety of materials.
Thus it is recognized that a frictional attenuation, .alpha..sub.a, of sound is directly proportional to frequency up to those frequencies where scattering effects occur. At scatter frequencies the attenuation becomes a function of mean grain diameter as well. Thus, at scatter frequencies attenuation includes both absorptive .alpha..sub.a and scatter effects, .alpha..sub.s. The latter, .alpha..sub.s, is dependent upon frequency and grain size in a manner generally described as:
(1) For .lambda.&gt;&gt;d, .alpha..sub.s varies according to d.sup.3 f.sup.4 PA1 (2) For .lambda..perspectiveto.d, .alpha..sub.s varies according to d f.sup.2 PA1 (3) For .lambda.&lt;d, .alpha..sub.s varies according to l/d
where .lambda. is the wavelength of the ultrasonic energy in the material, d the mean grain diameter and f the frequency of the ultrasonic energy.
Such known and predictable effect of homogeneous nonporous substances on ultrasonic energy has led to a specific ultrasonic energy backscatter technique for quantitativly measuring the grain size of a homogeneous specimen as described in the U.S. Pat. No. 4,026,157 to Goebbels. In accordance with this patent, sequential bursts of acoustic energy at respectively two different specific scatter frequencies are directed at a specimen for which the frequency dependency of the scatter attenuation is predictable. The transducer is oriented in a particular manner to enhance the generation of shear waves in the specimen, which may be so thin as to cause reflections from both upper and lower surfaces. Relative motion between the specimen and the transducer is maintained to average out interference maxima and minima. The acoustic backscatter energy is detected and used to derive amplitude attenuation plot for an apparently known acoustic path length. The measured attenuation at the two frequencies is then used to obtain a measurement of the grain size based upon the known frequency dependency of the attenuation at the two different frequencies.
A porous subsurface formation around a borehole does not exhibit a predictable frequency dependency like a carefully prepared specimen as described in the Goebbels patent. A specimen as described by the latter tends to be of a homogeneous character with closely spaced grains without voids or pores. In the exploration of a subsurface formation, however, one is interested in those rock formations where there exists a porosity capable of retaining hydrocarbons. Such porous subsurface formation is likely to be granular. The presence of porosity, however, affects the backscatter of ultrasonic energy, particularly at those frequencies which are highly sensitive to grain size. Furthermore, a subsurface formation is likely to have grains whose sizes may vary a great deal. Though for any narrow zone such grains may appear relatively consistent in size, the change in size from zone to zone as well as changes in orientation influence the amplitude and frequency of the backscatter signals. Hence, a direct measurement of the grain size as proposed in the Goebbels patent with different pulses at separate and discrete frequencies is not normally feasible for a porous subsurface formation.
A substantial body of prior art patents and literature exists related to ultrasonic nondestructive testing techniques. Such testing may include pulse echo techniques with spectrascopic investigations such as described, for example, in "Research Techniques in Nondestructive Testing" by R. S. Sharpe, published by Academic Press in 1970. With particular references to pages 43 through 53 therein, various spectra for different grain sizes of a material are illustrated. It is recognized that an accurate knowledge of the frequency response of the ultrasonic transducer is needed to evaluate the spectrum of echoes. The spectra are described as indicative of high attenuation characteristics of certain materials over particular frequencies. In theoretical treatises it has been shown that a single spherical object backscatters acoustic energy with maximum effect at a wavelength which approximates the diameter of the object. See, for example, articles "Numerical Computations of Elastic Scattering Cross-Sections" by G. Johnston and R. Truell, published in the Journal of Applied Physics, Volume 36, No. 11, pages 3466-3473, November, 1965 and "Analysis of Echoes from a Solid Elastic Sphere in Water" by R. Hickling and published in The Journal of the Acoustical Society of America, Vol. 34, No. 10, pages 1582-1592, October 1962; and "Ultrasonic Back-Scattering, A Method For Non-Destructive Structure Testing" by B. Fay, published at pages 51-53 in the 1976 Ultrasonics Symposium Proceedings of the IEEE, (Cat. No. 76 CH1120-5SU).
In prior art acoustic investigations of carefully prepared specimen at backscatter frequencies, the noise, i.e. the large peaks and valleys, both in the amplitude and the frequency domain, render meaningful analysis particularly difficult. When subsurface formations are investigated at backscatter frequencies, additional factors such as large grain size variations and porosity are introduced which strongly affect the acoustic backscatter.